Hello Tamás,
You are right, neither the MC33771C nor the MC33772C includes a dedicated identification register like WHO_AM_I. This means there is no simple or direct way to identify the BCC over SPI. Anyway, I guess you may try reading from a register that only exists or is valid on one of the BCCs. For example, read MEAS_CELL7 or higher. If the read returns valid data, the device is an MC33771C.
BRs, Tomas